In today's world, information and audio-visual content is transmitted over various mediums by a multitude of content providers. The mediums include standard over-the-air broadcasts systems, cable broadcast systems, satellite broadcast systems, and the Internet. Moreover, the sensitive financial information demands for secure and reliable storages and transmission.
Cryptography systems permit the protection of information and content which is sensitive, or intended only for a select audience. For example, a provider of satellite radio broadcasts may encrypt its transmission so that only authorized receivers may play the transmitted content.
One existing cryptography system which utilizes a technique known as ‘secret sharing’ is referenced as ‘threshold cryptography.’ A (k, n) threshold secret sharing scheme is one type of secret sharing system. A ‘secret sharing’ technique, developed by Adi Shamir, discusses the (k, n) threshold secret sharing technique using a polynomial function of the (k−1)th power to construct ‘n’ shares from a shared secret value. The technique satisfies following the two information entropy requirements: i) any ‘k’ or more shares can be used to reconstruct the secret, and ii) any k−1 or less shares could not reveal any information about the secret (See, E. D. Kamin, J. W. Greene, and M. E. Hellman, “On secret sharing systems,” IEEE Trans. Inform. Theory, vol. IT-29, no. 1, pp. 35-41, January 1983; A. Shamir, “How to share a secret,” Communications of the ACM, Vo. 22, No. 11, pp. 612-613, November 1979). Threshold cryptography uses the secret sharing technique to divide an encryption key into ‘n’ shares, such that any ‘k’ shares can be used to reconstruct the key.
Van Dijk et al. and Jackson et. al. have proposed extending the ‘secret sharing’ concept to share multiple secret(s) by using linear coding (See M. Van Dijk, “A linear construction of perfect secret sharing schemes”, in Advances in Cryptology—(EUROCRYPT '94): Workshop on the Theory and Application of Cryptographic Techniques Advances in Cryptology, A. De Santis, Ed., IACR. Perugia, Italy: Springer-Verlag, May 1994, pp. 23-35; W. A. Jackson and K. M. Martin, “Geometric secret sharing schemes and their duals”, Designs, Codes and Cryptography, vol. 4, no. 1, pp. 83-95, January 1994).
However, existing methods and systems for sharing multiple secrets suffer from large information overhead requirements.
Thus, there is presently a need for a system and method for sharing multiple secrets which has low information overhead, but yet maintains a high level of security.